Abstract

The uniform electron gas or UEG (also known as jellium) is one of the most fundamental models in condensed‐matter physics
and the cornerstone of the most popular approximation—the local‐density approximation—within density‐functional theory. In
this article, we provide a detailed review on the energetics of the UEG at high, intermediate, and low densities, and in one,
two, and three dimensions. We also report the best quantum Monte Carlo and symmetry‐broken Hartree‐Fock calculations available
in the literature for the UEG and discuss the phase diagrams of jellium. WIREs Comput Mol Sci 2016, 6:410–429. doi: 10.1002/wcms.1257

eHFFFrsζ as a function of rs for the paramagnetic and ferromagnetic fluid phases of 3‐jellium (see Eq. ). For rs>rsB, the ferromagnetic fluid becomes lower in energy than the paramagnetic fluid (Bloch transition). For rs<rs−, the ferromagnetic fluid becomes locally unstable toward depolarization, while for rs>rs+, the paramagnetic fluid becomes locally unstable toward polarization. The ‘hysteresis loop’ is indicated in red.

ecLDArs of 1‐jellium given by Eq. as a function of rs (solid line). Diffusion Monte Carlo results from Table are shown by black dots. The small‐rs expansion of Eq. (dashed line) and large‐rs approximation of Eq. (dotted line) are also shown.

Ziesche, P, Cioslowski, J. The three‐dimensional electron gas at the weak‐correlation limit: how peculiarities of the momentum distribution and the static structure factor give rise to logarithmic non‐analyticities in the kinetic and potential correlation energies. Physica A 2005, 356:598–608.